Least Common Multiple (LCM) of 142 and 180
The least common multiple (LCM) of 142 and 180 is 12780.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 142 and 180?
First, calculate the GCD of 142 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 180 = 0 remainder 142 |
| 2 | 180 ÷ 142 = 1 remainder 38 |
| 3 | 142 ÷ 38 = 3 remainder 28 |
| 4 | 38 ÷ 28 = 1 remainder 10 |
| 5 | 28 ÷ 10 = 2 remainder 8 |
| 6 | 10 ÷ 8 = 1 remainder 2 |
| 7 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 74 | 9102 |
| 182 and 17 | 3094 |
| 66 and 70 | 2310 |
| 105 and 61 | 6405 |
| 34 and 159 | 5406 |